The radioactive element carbon-14 has a half-life of 5750 years. a scientist determined that the bones from a mastodon had lost 78.5% of their carbon-14. how old were the bones at the time they were discovered?

Radioactive elements obey 1st order  kinetics,

For 1st order reaction, relation between rate constant (k) and half life [t(1/2)] is,
k = 

Also, for 1st order reaction, we have
t = 
 
Given that: the bones from a mastodon had lost 78.5% of their C14,
∴ initial conc. of C14 = 100%, conc. of C14 left after time 't' = 21.5%

∴t =  = 1.2758 X 10^4 hours

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